During the rolling of metal strips, because of the mechanical properties of roll stands and the flow properties of the rolled metal, so-called edge drop occurs, i.e., a flattening of the rolled strip at the edges. It is known e.g., from Japanese Patent Application No. 08 155 517 and from article "development of accurate control techniques of strip shop and edge-drop in cold rolling," Journal of the Iron and Steel Industry of Japan, Vol. 79, No. 3, 1993, pp. 388-94, to counteract the edge drop by means of so-called tapered rolls. To this end, the working rolls are curved in a suitable way. For a particularly precise driving of the so-called tapered rolls, the edge drop is measured upstream and downstream of the appropriate roll stand. However, these measurements are expensive, in particular when they have to be carried out for a plurality of roll stands. A further problem in the known method for reducing the edge drop is that the measures for reducing the edge drop must not lead to an impermissibly high tension in the edge region of the rolled strip nor to wavy edges. If the permissible tension in the edge region of the rolled strip is exceeded, then this can lead to an impermissible reduction in the quality of the rolled strip. In order to avoid this, in the case of the conventional method for reducing the edge drop, according to Japanese Patent Application No. 62 192 205, provision is made to measure the strip tension in the edge region of the rolled strip.